Thun 2006 - PhD Assessment of Fatigue Resistance And

DOCTORA L T H E S I S

Lule University of TechnologyDepartment of Civil and Environmental Engineering

Division of Structural Engineering

b: 978-91-85685-03-5|2006:65|: 102-15|: - -- 06 65 --

2006:65

Assessment of Fatigue Resistance and Strength in Existing Concrete Structures

Hkan Thun

Doctoral thesis 2006:65

Assessment of Fatigue Resistance and Strength in Existing Concrete Structures

Hkan Thun

Division of Structural Engineering Department of Civil & Environmental Engineering

Lule University of Technology SE-971 87 Lule

SwedenPhone (+) 46 920 49 10 00

Fax (+) 46 920 49 19 13 http://www.ltu.se

Assessment of Fatigue Resistance and Strength in Existing Concrete Structures HKAN THUN Avdelningen fr byggkonstruktion Institutionen fr samhllsbyggnad Lule tekniska universitet

Akademisk avhandling

som med vederbrligt tillstnd av Tekniska fakultetsnmnden vid Lule tekniska universitet fr avlggande av teknologie doktorsexamen, kommer att offentligt frsvaras i

universitetssal F1031, torsdagen den 21 december 2006, klockan 10.00

Fakultetsopponent: Professor Kent Gylltoft, Betongbyggnad, Chalmers Tekniska Hgskola, Gteborg

Betygsnmnd: Bitrdande professor emeritus Ralejs Tepfers, Betongbyggnad, Chalmers Tekniska Hgskola, Gteborg

Professor Sven Thelandersson, Konstruktionsteknik, Lunds Universitet, Lund

Adjungerad professor Bo Westerberg, Byggvetenskap, Kungliga Tekniska Hgsko-lan samt Tyrns AB, Stockholm

ISBN 978-91-85685-03-5 Doctoral Thesis 2006:65 ISSN 1402-1544 ISRN LTU-DT06/65SE

Preface

- i -

Preface

This thesis presents work that has been carried out at the Division of Structural Engineering, Department of Civil and Environmental Engineering at Lule University of Technology (LTU). The work has mainly been funded by Banverket (the Swedish National Rail Administration). Additional funding has been provided by Sustainable Bridges an Integrated Research Project within the European Community 6th Framework Program, the European Rail Research Institute (ERRI), The Development Fund of the Swedish Construction Industry (SBUF) and LTU.

First of all I would like to thank my supervisors Professor Lennart Elfgren, Dr. Tech. Ulf Ohlsson and Professor Thomas Olofsson for all their help and advice during the years.

My thanks are also due to the staff at TESTLAB, the laboratory at LTU. All of you have been involved in my work, but I would especially like to thank Mr. Georg Daneielsson, Mr. Hkan Johansson and Mr. Lars strm. They have performed, helped and advised me during all the tests/experiments during the past few years.

Additionally, I am very thankful to the colleagues and friends at the Division of Structural En-gineering for making the environment creative and joyful, especially Dr. Tech. Anders Carolin, Dr. Tech. Martin Nilsson, Lic. Tech. Hkan Nordin and Lic. Tech. Sofia Utsi who have been with me from the beginning of this journey.

Finally, writing a thesis is not possible without an extremely understanding family, thanks mother and father for helping us out during this period. I cannot express in words how grateful I am to Anna, my wife, for her support and patience during my work with the thesis. My kids, Cecilia and Alexander your smiles kept me going! Love you all!

Lule in November 2005

Hkan

The first draft of the text above was written on November 12, 2005, about 8 pm. An accident about one hour later, resulting in a bilateral hypoglossal nerve injury, postponed the completion of this preface until now. I am extremely thankful to my family Anna, Cecilia, Alexander, my parents and my brother Magnus and all of you, who have helped and supported me since the accident and made it possible for me to return to work and finish this thesis. Thank you all!

Lule in December 2006

Hkan

Abstract

- iii -

Abstract

During the last few decades, it has become more and more important to assess, maintain and strengthen structures like bridges, dams and buildings. This is mainly due to the fact that: (a) many structures are getting old and many have started to deteriorate, (b) there is sometimes a need to increase the load carrying capacity of an existing structure due to e.g. a demand for higher loads or (c) the cost to build new infrastructure is often higher than to repair/strengthen existing structures. Therefore it is of great interest to find methods to evaluate existing concrete structures in an efficient way. In this thesis parameters influencing the evaluation process have been investigated and analysed and the results are presented in the appended papers. Below, findings from the main areas are presented.

The development and variation of compressive and tensile strength of concrete are presented for old concrete bridges in Sweden. The mean increase in concrete compressive strength was about 70% for twenty bridges built during 1931-1962 (a rather high dispersion must be taken into consideration). The increase is related to the original 28-day concrete compressive strength which varied between 18 and 51 MPa. The compressive strength within a typical reinforced railway concrete trough bridge was approximately 15% higher in the longitudinal beams than in the bottom slab (measured on drilled cores).

A pullout test method, the Capo-test, has been examined as an alternative to drilled cores to determine the in-place concrete compressive strength. A strength relationship is proposed be-tween the compressive strength of a drilled core with the diameter and the height of about 100 mm, fcore, and the pullout force, F, from the Capo-test.

A probabilistic approach has been proposed for the evaluation of the shear force fatigue capac-ity of a concrete bridge slab. In the reliability analysis three different combinations of shear and fatigue models have been compared. The models have been used to determine the safety index (and the probability of failure) after another 5 or 25 years of traffic with higher axle loads (300 kN) than the bridge already has been exposed to. The most interesting combination seems to be the shear model of Hedman & Losberg (1975)/BBK04 (2004) and the fatigue model of Tepfers (1979).

Results and analyses are presented from cyclic uniaxial tensile tests performed on new and old concrete. The results from the tests indicate that the deformation criterion proposed by Balzs (1991) for bond slip may also be applied to plain concrete exposed to cyclic tensile load. A

Abstract

- iv -

method is proposed for how the deformation criterion may be used also for assessment of exist-ing structures.

The load carrying capacity of damaged prestressed concrete railway sleepers has been investi-gated. The sleepers had an age of five to ten years and the damage, in form of more or less severe cracking, is believed to be caused by delayed ettringite formation. The following tests have been performed: (a) bending capacity of the midsection and the rail section, (b) horizontal load capac-ity of the fastener, (c) control of the concrete properties and (d) fatigue capacity in bending of the rail section. A visual inspection and classification of the damages are also presented. The test results show that railway sleepers are quite robust. Small cracks do not seem to influence the load carrying capacity and it is first when the cracking is very severe that the load carrying capacity is reduced significantly.

Keywords: concrete, bridges, strength development, Capo-test, reliability analysis, tensile fa-tigue, deformation criterion, sleepers, delayed ettringite formation.

Sammanfattning

- v -

Sammanfattning

Under de senaste rtiondena har det blivit allt viktigare att tillstndsbedma, underhlla och frstrka konstruktioner ssom broar, dammar och byggnader. Huvudorsakerna till detta r: a) mnga konstruktioner r gamla och nedbrytning har pbrjats, b) ett behov av att ka kapacite-ten t.ex. hja axellasterna fr en jrnvgsbro samt c) kostnaden att bygga ny infrastruktur ofta r mycket hgre n att reparera eller frstrka en existerande konstruktion. Allt detta medfr att det r av strsta intresse att finna metoder att tillstndsbedma en konstruktion p ett s effektivt stt som mjligt. I denna avhandling har delar av tillstndsbedmningsprocessen studerats och analy-serats och resultatet finns presenterat i bifogade artiklar. Nedan fljer en kort beskrivning av de omrden som studerats.

Hllfasthetens variation i en konstruktion och dess utveckling ver tiden har studerats fr gam-la betongbroar. Fr de studerade broarna, byggda mellan 1931-1962, har tryckhllfastheten i genomsnitt kat med 70%. Denna kning r relaterad till 28-dygnshllfastheten d respektive bro byggdes och varierar mellan 18 och 51 MPa. Underskningar har visat att fr en standard trgbro r tryckhllfastheten ca 15% hgre i de lngsgende huvudbalkarna n i den bottenplatta de br.

En testmetod fr att kontrollera hllfastheten i en befintlig konstruktion, det s.k. Capo-testet, har studerats. Ett hllfasthetssamband presenteras mellan den utdragskraft som erhlls vid ett fr-sk med Capo-testet, F, och tryckhllfastheten, fcore, fr utborrade cylindrar med diametern och hjden ca 100 mm.

En sannolikhetsbaserad metod har anvnts fr att bedma tvrkraftskapaciteten vid utmattning av en bros betongplatta. Tre olika kombinationer av modeller fr utmattning och tvrkraft har underskts. Modellerna har anvnts fr att bestmma ett s.k. skerhetsindex, -index, fr 5 eller 25 r av ytterligare trafik med frhjd axellast, 30 ton. Av de kombinationer av modeller som studerats har tvrkraftsmodellen av Hedman & Losberg (1975)/BBK04 (2004) och utmattnings-modellen av Tepfers (1979) visat sig vara en intressant kombination.

Vidare redovisas resultat och analyser frn cykliska enaxiella dragfrsk fr ny respektive gam-mal betong. Resultaten indikerar att det deformationskriterium som freslagits av Balzs (1991) fr frankring ven r mjligt att anvnda fr oarmerad betong utsatt fr cyklisk dragbelastning. En metod r freslagen fr hur detta kan tillmpas vid tillstndsbedmning av konstruktioner.

Slutligen har brfrmgan fr skadade spnnbetongsliprar underskts. Sliprarna har haft en l-der av 5 till 10 r och skadorna de uppvisat r sprickbildning av varierande grad. Denna r tro-ligtvis orakad av s.k. frsenad ettringitbildning. Fljande frsk har utfrts: a) bjkapacitet i mitt-

Sammanfattning

- vi -

sektion och i rllge, (b) horisontell dragkapacitet av befstningar, (c) kontroll av betonghllfast-heten och (d) utmattningskapacitet i rllge. En visuell inspektion och klassificering av de skada-de sliprarna r ocks redovisad. Resultaten visar att sliprarna r relativt robusta, sm sprickor verkar inte pverka brfrmgan nmnvrt utan det r frst vid kraftig uppsprickning som br-frmgan reduceras avsevrt.

Nyckelord: betong, broar, hllfasthetsutveckling, Capo-test, sannolikhetsbaserad analys, utmatt-ning vid dragbelastning, deformationskriterium, sliprar, frsenad ettringitbildning.

Table of Contents

- vii -

Table of Contents

Preface...............................................................................................................i

Abstract ...........................................................................................................iii

Sammanfattning ................................................................................................v

Table of Contents ............................................................................................ vii

1 Introduction ................................................................................................. 11.1 Background - Assessment of Concrete Structures ........................................................11.2 Aims ...........................................................................................................................31.3 Limitations ..................................................................................................................31.4 Contents .....................................................................................................................3

2 In-place Concrete Strength ............................................................................ 52.1 Strength Development with Time...............................................................................52.2 Strength Variation .......................................................................................................62.3 Methods to Determine the in-place Concrete Strength ...............................................7

3 Reliability Analysis ...................................................................................... 133.1 Structural Reliability Analysis.................................................................................... 143.2 Target Reliability Index ............................................................................................ 17

4 Fatigue ....................................................................................................... 194.1 Fatigue in General..................................................................................................... 204.2 Steel ..........................................................................................................................214.3 Concrete Fatigue....................................................................................................... 21

4.3.1 Influencing Factors......................................................................................... 224.3.2 Refined Whler Curves ................................................................................. 22

4.4 Accumulated Fatigue Damage, Palmgren-Miner ....................................................... 26

5 Concrete Fatigue in Tension ........................................................................ 275.1 Tensile Behaviour of Concrete and Fracture Mechanics ............................................ 275.2 Fictitious Crack Model.............................................................................................. 295.3 Fatigue Capacity of Concrete in Tension .................................................................. 29

5.3.1 Material Models for Concrete Fatigue in Tension .......................................... 305.4 Fatigue Failure Criterion Based on Deformation ....................................................... 33

6 Assessment of a Railway Element Prestressed Sleepers ................................. 35

Table of Contents

- viii -

6.1 Background .............................................................................................................. 356.2 Results...................................................................................................................... 36

6.2.1 Load-carrying Capacity.................................................................................. 366.2.2 A Follow-up of Damaged Sleepers................................................................. 366.2.3 Wheel Load Distribution ............................................................................... 37

7 Summary of Appended Papers and Outlook...................................................39

References .......................................................................................................41

Paper A - Concrete Strength in Old Swedish Concrete Bridges ............................51

Paper B Determination of Concrete Compressive Strength with Pull-out Test ....65

Paper C Probabilistic Modelling of Shear Fatigue Capacity in a Reinforced Concrete Railway Bridge Slab ...........................................................81

Paper D Concrete Fatigue Capacity in Tension a Study of Deformations....... 103

Paper E Load Carrying Capacity of Cracked Concrete Railway Sleepers........... 135

APPENDIX A Result from Tensile Fatigue Tests ........................................... 151

Introduction

- 1 -

1 Introduction

1.1 Background - Assessment of Concrete Structures During the last few decades, it has become more and more important to assess, maintain and

strengthen structures like bridges, dams and buildings. This is mainly due to the fact that (a) many structures are getting old and many have started to deteriorate, (b) there is sometimes a need to increase the load carrying capacity of an existing structure due to e.g. a demand for higher loads or (c) the cost to build new infrastructure is often higher than to repair/strengthen existing structures. Therefore it is of great interest to find methods to evaluate existing concrete structures in an efficient way.

Research regarding condition evaluation of concrete structures has literally exploded lately. This is not only due to the reasons mentioned above but also due to the possibilities new tech-nique has brought. The procedure of inspection of e.g. a bridge, using new types of sensors and the fast development in data communications have made it possible to monitor structures con-tinuously, so-called Structural Health Monitoring, see e.g. Utsi et al. (2001), Olofsson et al. (2002), Hejll (2004) or Hejll & Tljsten (2005).

How can then an evaluation of e.g. a bridge be performed? What shall be checked? The ques-tions are many and in most cases not easy to answer. In Figure 1.1 an idea is presented of how such an evaluation could be performed. The procedure is suggested by the partners in the Euro-pean-project Sustainable Bridges - Assessment for Future Traffic Demands and Longer Lives. The aims of the project are to increase the transport capacity, the residual lifetime, allow higher traffic speeds for passenger traffic and enhance strengthening and repair systems of existing rail-way bridges. The consortium consists of 32 partners and it started in 2004 and will end in 2007, see Sustainable Bridges (2006).

The proposed procedure consists of three phases. The first, initial, phase is the simplest of them: an inspection at site, study of documents and simple calculations. The second, intermedi-ate, phase is a more refined check and might be more costly and time-consuming. It consists of e.g. strength tests and measuring at site of some parameters like strain or deflection or it can be monitoring for a longer period etc. With this information new and more detailed calculations could be performed. The third and last, enhanced, phase is an even more refined check. The question that must be answered after each phase is if the structure is safe and what action must be taken. In the end one of the following actions must be considered:

Introduction

- 2 -

Unchanged use of the structure?

Supervise the structure e.g. measurement of the strain development over a longer time?

Strengthen the structure with e.g. carbon fibre reinforced polymers, see e.g. Carolin (2003), Tljsten & Carolin (1999) or the Swedish guidelines for FRP-strengthening in Tl-jsten (2004)?

Demolish the structure and build a new one?

As can be seen in the figure there are several influencing factors that could be considered. If the point material investigations, see phase 2, is used as an example some of the factors that could be checked are: in-place concrete strength, cover of the reinforcement, amount and qual-ity of the reinforcement, degree of degradation etc. If every point in Figure 1.1 is broken down like this it is easy to see that condition evaluation of a bridge is a difficult and in many cases a time-consuming task.

Doubts

PHASE 1 Site visit

Study of documents Simple calculation

PHASE 2 Material investigations

Detailed calculations/analysis Further inspections and monitoring

PHASE 3 Refined

calculations/analyses Laboratory examinations and

field testing Statistical modelling

Reliability-based assessment

Simple strengthening

of bridge

Update maintenance, inspection and

monitoring strategy

Redefine use and update maintenance,

inspection and monitoring strategy

Demolition of bridge

Strengtheningof bridge

Unchanged use of bridge

Doubts confirmed? Yes

Yes Yes

Yes

No No

No

No

Compliance with codes and

regulations?

Simple repair or strengthening

solve the problem?

Sufficient load capacity? Acceptable

serviceability?

PHASE 2 - INTERMEDIATE

PHASE 1 - INITIAL

PHASE 3 - ENHANCED

Figure 1.1 Suggested flow-chart for reassessment of existing bridges proposed by the EU-project Sustainable Bridges (2006).

Some of the checks in Figure 1.1 are not easy to perform, but if they are made, they often give very valuable information. Field testing for example, see phase 3 in Figure 1.1, has in earlier research projects at LTU shown to be a very valuable instrument when evaluating the condition of a bridge, see Paulsson et al. (1996,1997).

Regarding the analysis methods, statistical modelling and reliability-based methods are perhaps the most suitable methods when evaluating e.g. a concrete bridge. These types of analysis meth-ods have been used in an assessment project of a bridge in northern Sweden, the Luossajokk

Introduction

- 3 -

Bridge, see Enochsson et al. (2002, 2005). Instead of strengthening the bridge, the result from the reliability analysis showed that the bridge could be kept as it was but with continuous moni-toring in this case measuring of the strain development in the reinforcement bars.

1.2 AimsThe aim is to study some of the factors that are of importance in the assessment process of an

existing concrete structure, see Figure 1.1.

Firstly, to investigate the in-place concrete strength in an existing bridge. What variation of concrete strength can be expected? Can an increase of concrete compressive strength be ex-pected for old concrete structures and what methods to investigate the strength are available.

Secondly, to present a method that can be used for shear fatigue evaluation of concrete bridge slabs and to study the influence of different factors on this method.

Thirdly, to investigate a deformation criterion and to verify it for plain concrete exposed to cyclic loading in tension. Furthermore to investigate if it can be used on an entire structure.

Fourthly, the thesis aims to investigate methods to evaluate damaged railway sleepers and de-termine their remaining load carrying capacity.

1.3 Limitations When evaluating an existing structure there are several factors that influence the load carrying

capacity. In this thesis the study has been limited to investigate some of the aspects of in-place concrete strength. The fatigue phenomenon has only been investigated with respect to plain concrete exposed to cyclic load in tension.

1.4 ContentsThis thesis consists of five papers. Background material, theories etc. to every subject that is

investigated are presented in the following chapters:

In Chapter 2 a brief introduction is presented to in-place concrete strength, i.e. the develop-ment, variation and testing of tensile and compressive strength for old reinforced concrete bridges. This subject is further presented in paper A and B where analyses and test results can be found of concrete trough bridges.

Chapter 3 contains a brief introduction to reliability analysis of structures. The method has been used in the study presented in paper C to determine a safety index for a typical railway bridge exposed to fatigue load in tension.

In Chapter 4 fatigue of concrete structures in general is described and in Chapter 5 concrete fatigue in tension is described. The intentions with these parts are to present research that is of special interest to the theme of this thesis. Background to the fatigue behaviour of concrete is presented. A deformation criterion for fatigue failure in concrete is also described. Some of the models that are presented are used in papers C, D and E.

In Chapter 6 an investigation of prestressed concrete sleepers is presented.

Chapter 7 includes a short summary of each appended paper and an outlook.

Introduction

- 4 -

Appendix A includes results from the fatigue tests presented in paper D Concrete Fatigue Capacity in Tension- a Study of Deformations.

Appended papers:

Paper A is titled Concrete Strength in Old Swedish Concrete Bridges by Hkan Thun, Ulf Ohlsson and Lennart Elfgren.

Paper B is titled Determination of Concrete Compressive Strength with Pullout Test by Hkan Thun, Ulf Ohlsson and Lennart Elfgren.

Paper C is titled Probabilistic Modelling of the Shear Fatigue Capacity by Hkan Thun, Ulf Ohlsson and Lennart Elfgren.

Paper D is titled Concrete Fatigue Capacity in Tension a Study of Deformations by Hkan Thun, Ulf Ohlsson and Lennart Elfgren.

Hkan Thuns contribution to the papers A, B, C and D is planning a large part of the tests, participating in most of them, evaluating the data, performing the analyses and finally writing the papers including drawing some of the figures. Guidance and comments have been given by the co-authors Dr. Tech. Ulf Ohlsson and Professor Lennart Elfgren throughout the project.

Paper E is titled Load Carrying Capacity of Cracked Concrete Railway Sleepers by Hkan Thun, Sofia Utsi and Lennart Elfgren, and is submitted to Structural Concrete, Journal of the fib.The laboratory tests of the bending capacity of the midsection and the rail section have been performed by Sofia Utsi while the tests of the horizontal load carrying capacity of the fastener (except for one of the tests) and the fatigue tests have been performed by Hkan Thun. Hkan Thun and Sofia Utsi have written the paper and drawing the figures with guidance and com-ments by Professor Lennart Elfgren.

In-place Concrete Strength

- 5 -

2 In-place Concrete Strength

Different aspects of the subjects presented in this chapter have been used/investigated in paper A and B where the in-place concrete strength variation and concrete strength development with time have been investigated together with a comparison between different methods to determine the in-place concrete strength. An introduction to different aspects of in-place concrete testing can be found in e.g. Bungey & Millard (1996), Carino (2004) or Thelandersson (2007) and is in this chapter described briefly.

2.1 Strength Development with Time When assessing e.g. a bridge, several factors are examined and one of them which is important

is the concrete strength. Studies found in the literature show that the compressive strength of concrete could increase with age for old structures. This is in turn a huge bonus since natures own strengthening is less expensive, actually free of charge, than strengthening with e.g. carbon fibre would be. The phenomenon has been investigated for Swedish bridges and the findings are presented in paper A.

Why the increase then? Several reasons are possible. According to Johansson (2005), the most likely has to do with the properties of the Portland cements used during the 1930s and 1940s. During this period the Portland cements had a different ratio of dicalcium silicate (C2S) to trical-cium silicate (C3S) and were more coarsely ground (i.e. the fineness was lower) compared to the Portland cements of today, see e.g. Lea (1970), Taylor (2002) or Neville (1995). The two sili-cates are primarily responsible for the strength of the hydrated cement paste: where the trical-cium silicate (C3S) influences the early strength and the dicalcium silicate (C2S) the later increase in strength. The trend during the last few decades has been that, due to improved manufacturing methods, the amount of tricalcium silicate has increased which results in higher early compres-sive strength (in combination with a higher fineness) and a lower increase in long-term strength. In this context it must also be mentioned that the concrete compressive strength of course can decrease with time due to e.g. environmentally caused degradation.

An example is given in Wood (1991) where long-term data are compiled from four different studies initiated between 1940 and 1956 by the Portland Cement Association. In the investiga-tion data on the variation of concrete compressive strength, flexural stiffness and modulus of elasticity with time are presented. The cement, Type I according to ASTM, used in one of the studies was produced in 1947 and the potential compound composition of C2S and C3S was about 16-30% and 43-58 % respectively. The cement was also coarser compared to modern


- 6 -

cements. After 20 years the mean concrete compressive strength was approximately 40 % higher than the 28-day strengths (the percentage level is derived manually from graphs in Wood (1991)). The difference between the concrete compressive strength development of specimens cured in a moist room and specimens stored outside were slight. From the results Wood could also conclude that the compressive strength of concrete increased with a decrease in the water to cement ratio. Other examples are given in Washa & Wendt (1975), Walz (1976) or Washa et al. (1989).

No literature regarding a similar increase of the tensile strength of concrete with time has been found.

2.2 Strength Variation It is a well-known fact that there is a variation of concrete properties within a member of a

structure. This variation may be due to differences in concrete compaction and curing and/or differences in the quality of the concrete delivered. In the literature one can find that the bottom parts are usually better compacted with higher density than the top parts, where the percentage of ballast may be smaller. This is due to the influence of the gravity force and the stability of the concrete mixture. Strength variation has been investigated for Swedish bridges and the findings are presented in paper A.

The variation of in-place concrete strength in a structure could, according to Bartlett & Mac-Gregor (1999), be due to:

Within-batch variation (e.g. the randomness of the strength of different parts included in a single batch of concrete)

Batch-to-batch variation (factors that could vary between batches e.g. difference in amounts, properties of the components, mixing procedures)

Systematic within-member variation (if the consolidation, water content or curing condi-tions vary in a consistent manner)

Systematic between-member strength variation (could be due to different curing condi-tions, e.g. different ambient temperature for a column on different floors)

Strength variation between different types of members

If the concrete strength property is considered, the strength variations that can be found in a member of a structure are different depending on if it is e.g. a wall or a slab. According to Bungey & Millard (1996) the variation between the top and the bottom for a beam can be up to 40% and for a slab up to 20% (here the loss in strength is concentrated to the top 50 mm), see Figure 2.1. Bungey & Millard point out that the curves in Figure 2.1 are based on numerous reports of non-destructive testing and can only be regarded as indicating general trends which may be expected. A variation of strength in a member, i.e. higher in the bottom than in the top, could also be found in e.g. Bartlett & MacGregor (1999).


- 7 -

Slab

Beam

Wall

Column

Top

3/4

Mid

1/4

Bottom 0 25 50 75 10 125

Relative strength (%)

Loca

tion

with

in m

embe

r

Figure 2.1 Typical within-member variations of relative strength for normal concretes according to member type, from Bungey & Millard (1996).

2.3 Methods to Determine the in-place Concrete Strength There are several methods to test the in-place concrete strength of a structure. The methods

can be divided into three basic categories, depending on the type of damage they cause on the structure:

non-destructive testing (causes no damage on the test object)

semi-destructive testing (causes minor local surface damage on the test object)

destructive testing (causes major damage on the test object)

However, the boundaries between the first two named above, are slightly indistinct. Accord-ing to The American Society for Non-destructive Testing (ASNT) the definition of non-destructive testing is Nondestructive testing (NDT) has been defined as comprising those test methods used to examine an object, material or system without impairing its future usefulness. What makes the boundaries vague, according to ASNT, is the words future usefulness. Some methods involve taking samples from the test object and would then make the methods destruc-tive but since the samples are often taken in parts that do not reduce future usefulness of the object - it could be argued that the method is non-destructive.

In this investigation two methods have been used to determine the in-place concrete strength of reinforced concrete railway trough bridges; drilled cores and the so-called Capo-test. They both belong to the category semi-destructive testing at least the Capo-test which is a so-called pullout method.

To drill out and test cores is a common method to estimate the in-place strength of a concrete structure. Most countries have adopted standard procedures for how a core should be prepared, stored, etc. before testing.

The Capo-test (from cut and pull out-test) is a method to determine the concrete strength of the cover-layer for an existing structure. It was developed in Denmark by C German Petersen and E Poulsen in the middle of the 1970s, see e.g. German Petersen & Poulsen (1993). The test procedure of the Capo-test consists of drilling a 65 mm deep hole with a diameter of 18 mm using a water-cooled diamond bit, see Figure 2.2a. Then a 25 mm recess is made at a depth of


- 8 -

25 mm using a portable router. An expandable split steel ring is inserted through the hole in the recess and expanded by means of a special tool. Finally the ring is pulled through a 55 mm counter pressure placed concentrically on the surface. The pullout force, F, is measured by the pull machine and can be converted into concrete compressive strength, fc, by means of calibra-tion charts provided by German Petersen & Poulsen (1993). A description of the method can also be found in e.g. Bungey & Millard (1996). An example of the cone that is extracted after a performed test is shown in Figure 2.2b.

If the two methods are compared in general, the Capo-test is a simpler and less expensive test to perform compared to drilled cores on the bridges. The Capo-test has the advantage that the equipment is lighter and easier to transport to the bridge compared with the equipment used for drilling cores. This was one of the key-advantages since many of the bridges in this investigation could only be reached by train or on foot. Important in this case was also the less damage the Capo-test inflicts on the bridges.

To hydraulic pull machine

Counter pressure (support)

Failure coneExpandable split steel ring (disc)

Drilled hole

Recess

25 55

[mm]

25

18

a) b)

Figure 2.2 a) Schematic drawing of the Capo-test, based on German Petersen & Poulsen (1993), Bungey & Millard (1996) and Carino (2004) and b) Picture showing the extracted cone after a performed Capo-test. Photo from Johansson (2000).

The Capo-test correlation charts for concrete compressive strength and the pullout force are based on several laboratory and field studies made by the manufacturer as well as by other re-searchers. In most cases it is the results from the Lok-test (see below) that are the basis of the correlations charts, but in some cases also the Capo-test. The suggested general correlation for standard 150 mm cubes is shown in Eqs. (1) and (2) in Figure 2.3, from German Petersen (1997).

Rockstrm & Molin (1989) have shown that the relation suggested by German Petersen (1997), see Figure 2.3, can be improved when the test object is an old structure, i.e. an old road bridge. They got higher concrete strengths according to Eq. (1) in Figure 2.3, when they per-formed tests with both the Capo-test and drilled cores on six road bridges that had ages up to 54 years.

The studies in this thesis of the Capo-test confirm the findings by Rockstrm & Molin, i.e. a need for an improved strength relation between the pullout force from the Capo-test and the compressive strength of a drilled core with the diameter and height of 100 mm. The proposal could be found in paper B.


- 9 -

10 20 30 40 50 60 70 80 90 100 110Cube Strength, fc', 100100 mm Core Strength [MPa]

0

10

20

30

40

50

60

70

Lok-

Stre

ngth

& C

apo-

Stre

ngth

, F [k

N] General correlation 150 mm cubes:

Eq. (1): F = 0.71 . fc' + 2.0 50 MPaEq. (2): F = 0.63 . fc' + 6.0 50 MPa

Rockstrm & Molin correlation:Eq. (3): F = 0.55 . fc' + 3.16

Figure 2.3 Correlation between Capo-test and drilled cores with the height and the diameter of 100 mm, trimmed and air-cured 3 days before testing, made by Rockstrm & Molin (1989) based on 5 old Swedish bridges. The correlation is compared with the general correlation for 150 mm standard cubes suggested by the manufacturer. From German Petersen (1997).

The Capo-test is a further development of the so-called Lok-test where the pullout bolt is em-bedded in fresh concrete. Carino (2004) reports that the first time a description of the pullout test method was presented in the literature, was in 1938 in a paper by Skramtajew (1938) where different test methods to measure the in-place concrete strength were reviewed. Later on in 1944 Tremper (1944) published research results of pullout tests with a design similar to the de-sign described by Skramtajew. In 1962 Kierkegaard-Hansen (1975) initiated a research pro-gramme and the result of the work led to the test-system known as the Lok-test. Kierkegaard-Hansen improved the original design by introducing the support ring (also called the bearing ring or reaction ring) - this support ring was not used in the tests reported by Skramtajew and Tremper. For more detailed information regarding the history of the pullout test method see e.g. Carino (2004).

From the end of the 1970s until the beginning of the 1990s the Lok-test and similar methods were subject to discussions in the concrete society, particularly regarding what property that is actually measured in a pullout test. In the literature different theories have been presented over the years. One of them is a non-linear finite element analysis presented in Ottosen (1981). His analysis of the Lok-test showed that large compressive forces run from the disc in a rather narrow band towards the support and this constitutes the load carrying mechanism. Ottosen concluded further, that the failure in a Lok-Test is caused by the crushing of the concrete and not by crack-ing. Therefore, the force that is needed in a Lok-test to extract the embedded disc directly de-pends on the compressive strength of the concrete.

Stone & Carino (1983) raised doubts regarding the thesis with narrow bands proposed by Ot-tosen (1981). The reasons for this were that the model assumed a perfect bond between the pullout disc and the surrounding concrete which they believed to be unlikely since the pullout insert is often coated with oil prior to casting and that no evidence of narrow bands had been detected in physical tests. In their own study they carried out large-scale pullout tests and they identified three distinct phases in a failure sequence of a pullout test.

Phase 1: initiation of circumferential cracking near the upper edge of the disc at approxi-mately 1/3 of ultimate load.


- 10 -

Phase 2: completion of circumferential cracking from disc edge to support ring at approxi-mately 2/3 of the ultimate load.

Phase 3: shear failure of matrix and degradation of aggregate interlock beginning at about 80% of ultimate load.

They proposed that ultimate failure was probably due to pullout from the matrix of the bridg-ing aggregate particles.

The idea by Stone & Carino (1983), that aggregate-interlock across the failure surface is the reason for the load capacity above the 64% mentioned in Ottosen (1981), was rejected in Yener (1994), since aggregate interlocking would be very sensitive to different types of aggregate. This would in turn had led to reports of high within-test variations in performed tests. The large scale test by Stone & Carino was also commented by Krenchel & Shah (1985). They pointed out that the results in Stone & Carino do not necessarily correspond to the conventional pullout test since they did not scale up the maximum aggregate size, only the dimensions of the test speci-mens.

In 1984 Stone & Carino (1984) presented an axisymmetric linear elastic finite element analysis and compared it with their experimental results presented in Stone & Carino (1983). They con-cluded that because the complex three-dimensional stress states produced during the test (there are no regions where the stresses are simple unidirectional tensile or compressive stresses), it was unlikely that the pullout strength was directly related to the compressive strength and that an alternative explanation was needed for the observed correlation between the two strengths. They proposed that the correlation between the calculated principal tensile stress trajectories and the measured failure surface geometry from experiments suggested that formation of the complete failure surface is governed primarily by the tensile strength of the mortar. They proposed that this is the explanation of the correlation between the pullout strength and the compressive strength of concrete, i.e. both are governed primarily by the tensile strength of he mortar.

The method used by Stone & Carino (1984) was questioned by Yener (1994), since the crack-ing in concrete in a pullout test initiates at a load which is only a small fraction of the failure load, an interpretation drawn from a linear elastic analysis does not provide sufficient information regarding the progressive failure of the concrete medium. Further, Yener states that, it does not provide a clear insight into the interesting phenomenon that, although at 65 percent of the ulti-mate load and the failure surface is already formed, concrete still possesses additional strength.

Yener (1994) described the progressive failure of concrete subjected to pullout tests based on a plastic-fracture finite element analysis. Based on numerical results, Yeners examination of the stress distribution in the uncracked and cracked concrete, indicated that the behaviour of con-crete subjected to a pullout force in a Lok-Test is primarily controlled by combined compression and bending actions, where the bending actions are pronounced in the latter stages of the load-ing. Yener also pointed out that it may not be appropriate to describe the complex state of stress in a pullout test by a uniaxial mode of failure. Based on his study, Yener concluded that the reasonable and consistent experimental correlation between the pullout force and the compres-sive strength of concrete is explained by indicating that the residual strength in pullout tests is a consequence of crushing of the concrete close to the support.

If the results from the different theories described above are compared there are, however, some similarities. In all investigations a complex stress state during the pullout test has been con-firmed. The cracking initiates at a small fraction of the ultimate load and two major cracks are present: a circumferential crack that starts to develop at approximately 25-30% of the ultimate load, see Figure 2.4 and moves toward the support ring and a secondary circumferential crack


- 11 -

that forms the completed failure surface (which is reached at approximately 60-70% of ultimate load). A thing common for all studies of the Capo-test, is that a fairly good correlation has been found to exist between the pullout force and the concrete compressive strength.

Counter pressure or reaction ring or support

Failure cone

Expandable split steel ring

First circumferential crack

Second circumferential crack

Figure 2.4 Schematic drawing of the circumferential cracks from Lok-test/Capo-test. Based on Carino (2004).

All investigations mentioned above have studied the Lok-test where the pullout bolt is inserted before casting. The Capo-test, which has been used in this investigation, has not been a subject for as many studies. The main difference between the two test methods, regarding the failure process, is that no bond exists between the steel disc and the surrounding concrete in the Capo-test and that the geometry is a bit different. Otherwise, the failure process should be similar.

If the failure surface of the extracted failure cones from the Capo-tests performed in this thesis is studied and compared to the failure theories in the literature, there are some similarities as well as discrepancies. The failure has in most cases not been only due to pullout from the matrix of the bridging aggregate particles, as formulated by Stone & Carino (1983). Instead the failure has in many cases been due to failure of the ballast which indicates a good bond between the ballast and the cement paste in these cases, i.e. high strength of the mortar (the compressive strength of concrete has been high in most cases). It also indicates that the failure in this case supports the theories that the ultimate failure could be due to e.g. crushing of the concrete rather than aggre-gate interlocking at least when the compressive strength of the tested concrete is high. The tensile strength of the concrete does seem to have an impact on the failure mechanism. This is indicated if the general shape of the proposed modified correlation curve between the compres-sive strength of drilled cores and the pullout strength from the Capo-test is studied, see paper B. The shape agrees with the general form of the correlation between the compressive strength of concrete and the tensile strength of concrete that could be found in the literature. Perhaps the failure type changes, depending on the strength of the concrete, during the test, compare with Figure 2.3. However, these ideas are just speculations since the failure itself has not been investi-gated in this thesis.

As mentioned earlier, the Capo-test is intended to determine the strength of the cover-layer, but in this thesis efforts have been made to use it as an alternative to drilled cores to determine the in-place concrete compressive strength.

Reliability Analysis

- 13 -

3 Reliability Analysis

In this chapter reliability analysis is described briefly and in paper C the method has been used on a railway concrete bridge in order to determine the remaining shear fatigue capacity. An introduction to reliability analysis can be found in Schneider (1997) and Diamantides (2001). General textbooks of reliability analysis have been written by e.g. Thoft-Christensen & Baker (1982) and Ditlevsen & Madsen (1996). Swedish examples where a reliability analysis has been applied in practice in structural analysis are given in Fahleson (1995), Enochsson (2002), Jeppsson (2003) and Nilsson (2003).

In Figure 3.1 an illustration proposed by Schneider (1997) is shown that in general describes the process of safety evaluation of an existing structure. The need to assess the reliability of an existing structure can be due to many reasons, but as mentioned in Schneider (1997), the reasons can be traced back to doubts about the safety or the reliability of the structure. The aim of the reliability assessment of an existing structure is to produce proof that it will function safely over a specified residual service life, see Diamantides (2001).

What are the definitions of the terms safety and reliability? The term reliability can, according to Schneider (1997), be defined as the probability that an item or facility will perform its in-tended function for a specified period of time, under defined conditions. The term safety is defined with respect to safety for people. Schneider (1997) exemplifies with the Swiss Standard, where safety is defined as The term safety in the SIA Building Code is primarily related to the safety for people affected by structural failures. Schneider further emphasizes that in the defini-tion of safety, it is not the structure as such that is designated safe, but rather the people in its area of influence.

In Figure 3.1 an illustration of the engineers situation in the assessment of a structures safety is shown, Schneider (1997). The question that must be answered is if the structure is safe enough and depending on what answer is given, different actions have to be taken, see Figure 3.1 (com-pare with Figure 1.1).


- 14 -

Inspection limited means, small fee

Additional investigations

Do nothing

Intensifymonitoring

Reduceloads

Strengthenstructure

Demolishstructure

Safe? no

?

yes Doubts

Figure 3.1 Illustration of the engineers situation in the assessment of a structures safety, from Schneider (1997).

Schneider further writes that the assessment of structural reliability of an existing structure is a difficult task since statements about its possible behaviour under conditions of extreme loading must be made. Such conditions normally lie outside the range of experience gained from observ-ing the behaviour under service loads. Another important factor when assessing existing struc-tures is that it is essential to know for how long the structure is intended to serve its purpose, the so-called residual service life.

According to Schneider (1997) experience has shown that the assessment procedure is gained by subdividing the scheme given in Figure 3.1 into three phases where each phase should be completed before the next starts. The subdivided scheme presented by Schneider is very similar to the one shown in Figure 1.1, but with a few significant differences. Schneider is of the opin-ion that each phase should begin with a precisely formulated contract, usually in written form, which has been made by the consulting engineer and the client together. Each phase should end with a report leaving the owner with his responsibility and freedom of decision, where this free-dom is restricted by the recommendations of the engineer and the requirements of the law. Schneider also suggests, which is interesting, that phase 2 and 3 are carried out by a team of engineers (experts) in contrast to the first phase, a preliminary assessment, which could be done by one engineer alone. For more details about the procedures see Schneider (1997) or Diaman-tides (2001).

3.1 Structural Reliability Analysis What methods can be used to determine the safety of an existing structure? Is it perhaps ap-

propriate to use the same methods as when the structure was built? An answer to these two questions can be given if the difference between the two situations is studied. As pointed out by Melchers (1999) a reason for not using design codes in an assessment situation is that a design code needs to allow for uncertainties in the design and construction process and these uncertain-ties will have been realised in the finished structure. Another difference between design of a new structure and assessment of an existing structure is that the information available at the two situa-tions is different. A critical aspect, as Schneider (1997) points out, when assessing the structural safety is the rather poor information about the condition of certain structural elements, e.g. with respect to corrosion or fatigue. However, this can be true for the examples given by Schneider, but on the other hand, other information is known e.g. some of the design loads can perhaps be excluded, the material strength can be investigated, dimensions could be measured etc.

Another question that can be discussed is: if reliability methods are chosen for evaluation of a bridge - what analytical models shall then be used e.g. to calculate the fatigue capacity of the concrete? The problem that arises if the analytical models in the codes are used could be exem-plified with the study performed by Johansson (2004), where an investigation was performed to


- 15 -

see if present concrete codes were underestimating the fatigue capacity. Fatigue tests were per-formed on beams with the length of 2.5 m (and 2 m), width of 0.8 m and the thickness of 0.2 m and the results were compared to calculations according to BBK94 (1994,1996), CEB-FIP (1993) and EC2-2 (1996). Among other things the result was compared to the predictions ac-cording to the above-mentioned concrete design codes. It was then found that CEB-FIP (1993) was extremely conservative regarding fatigue capacity in shear and that BBK (1994, 1996) re-sulted in very conservative fatigue life predictions of fatigue of concrete in compression. This shows that if the analytical models presented in the codes are used in a reliability analysis, they can give an unnecessary conservative result as in the case with fatigue capacity where big safety factors are included.

What procedure is used when a structure is designed? In many areas the so-called allowable stress format is still used. This design criterion limits the maximum stress to be less or equal to allowable values prescribed in standards or codes. In Schneider (1997) the safety condition is written as:

allowed max (1)

In Sweden, and other countries as well, the so-called partial factor format is primarily used and it applies factors to all relevant design parameters. The partial factor format could according to Fahleson (1995) be described as a semi-probabilistic method since the partial coefficients are calibrated, in contrast to e.g. the allowable stress format, against probabilistic methods so that the method will give a reliability close to a predetermined reliability. In the Swedish Building Code, BKR03 (2003), it is written in the following way:

( ) ( )d d d S d d R, , , , , ,S F f a R f a C (2) where d indicates design value, S is effect of action, R is resistance. F is action, f is the material

property, a is geometrical parameters, S is partial factor for the analytical model for the effect of action, R is partial factor for the analytical model for resistance and finally C is a limiting value e.g. the greatest deformation for which the performance requirement is satisfied.

A method that can also be used for design of new structures is a probabilistic method where the probability of failure is calculated. This method is perhaps even more suitable to use in as-sessment of existing structures since the method uses available information regarding a specific structure. The factors that influence the problem are introduced as random variables with their distribution types and their respective parameters.

In Melchers (1999) the methods to calculate the probability of failure are divided into the fol-lowing techniques: direct integration (possible only in some special cases), numerical integration (such as the Monte-Carlo simulation) or second-moment and transformation methods. In this paper a brief description of structural reliability analysis will be presented and a full description of the mathematical backgrounds and theories of structural reliability analysis can be found in e.g. Thoft-Christensen & Baker (1982), Schneider (1997), Ditlevsen & Madsen (1996) or Melchers (1999).

In Melchers (1999) structural reliability analysis is explained with the basic structural reliability problem consisting of one load function, S, and one resistance function, R. They are both de-scribed by a known probability density function fS() and fR() respectively. The probability of failure, pf, is given by:

( )f 0p P R S= (3)


- 16 -

The principle is often described with an example where it is possible to solve the reliability problem analytically. This can be performed when R and S are two normally distributed random variables with means R and S and variances R2 and S2 respectively, see Figure 3.2. The safety margin M = R - S then has a mean and a variance according to:

M R S = (4)

2 2 2Z R S = + (5)

Eq. (3) could then be written as:

( ) ( )( ) ( )R SM

f 1/22 2MS R

00 ( 0)p P R S P M

= = = = = +

(6)

here ( ) is the standard normal distribution function with zero mean and unit variance and is given in normal distribution tables. The higher is, the higher is the safety of the structure. =M/M is defined as the so-called safety index. can also be expressed in words as the measure, see Figure 3.2, in standard deviation M units, from the mean value, M, to the failure limit M = 0. The random variable M = R - S is also shown in Figure 3.2, in which the failure region M 0 is equal to the shaded area.

fR()

fS()

S

R

S RM r,s0

m0

M

M

fM() pf(< 0)

MFigure 3.2 Probability density functions for the parameters, R, S and M i.e. fR(), fS() and fM().Based on Schneider (1997).

The so-called weighting factors (or sensitivity factors), i, are of special interest, since they show what importance the corresponding variable has in the value of the probability of failure. For the example above these can be calculated from, Schneider (1997):

= =

+ +

R SR S

2 2 2 2R S R S

; (7)

where 2 2R S 1 + = . The values of these sensitivity factors are between 1 and -1. They are positive for favourable parameters (resistance) and negative for unfavourable (loads).


- 17 -

One method, which belongs to the numerical integration methods, of solving the expression for the probability of failure, pf, is to use so-called Monte-Carlo simulation. The method uses random sampling to simulate a large number of experiments and register the result. Random sampling is performed for all involved stochastic variables to obtain random sample values of the stochastic variables which are then used to check R-S. This is repeated many times and the num-ber of times R-S is less or equal to zero, i.e. when the structure has failed, are registered and the probability of failure, pf, is given as:

failf

total

np

N= (8)

where Ntotal is the total number of trials and nfail is the number of trials where R-S 0.

In JCSS (2001) it is stated that there are mainly two different fatigue models that are used in a reliability analysis, i.e. S-N models based on experiments or fracture mechanic models. If e.g. the S-N model is used, Melchers (1999) points out that e.g. constants used in the models must be introduced as random variables (combined with estimates of the uncertainties of the parameters) and the model itself must give a realistic estimation of the fatigue life. This compared to e.g. the design codes where constants could be found in tables and the model often gives conservative result. If this is commented, i.e. the introduction of the constants as random variables and as realistic models as possible, it seems to be something that is not something specific only to fatigue analyses, but something that is a must for all reliability analyses.

In this thesis the computer programme Variable Processor, VaP, developed by Petschascher (1993) and Schneider (1997), has been used to determine the probability of failure, pf, or the so-called safety index . The program uses, among others, the First Order Reliability Method (FORM) and the Monte Carlo method in the analysis.

3.2 Target Reliability Index One way to determine if a structure is safe enough is to compare the calculated reliability in-

dex, , to a so-called target reliability index, 0, that represents the safety level of the existing codes, see Schneider (1997).

Values of this target reliability index, 0, are given in e.g. the Probabilistic Model Code issued by the Joint Committee on Structural Safety, JCSS (2001). In the Swedish Design Regulation, BKR03 (2003), the following target reliability index, 0, is given for a reference period of 1 year:

0 > 3.7 for Safety Class 1 (corresponds to the probability of failure, pf = 1 10-4)0 > 4.3 for Safety Class 2 (corresponds to the probability of failure, pf = 8 10-6)0 > 4.8 for Safety Class 3 (corresponds to the probability of failure, pf = 8 10-7 ) The safety classes above are in turn connected to the possible injury to persons:

Safety Class 1 (low), little risk of serious injury to persons Safety Class 2 (normal), some risk of serious injury to persons Safety Class 3 (high), great risk of serious injury to persons

Fatigue

- 19 -

4 Fatigue

In this chapter fatigue in general is described. The parts that have been chosen are ones that are common and they show some of the different factors that have been studied over the years. Fatigue analysis has been described in several textbooks for different materials over the years, see e.g. Frost et al. (1974), Mallet (1991), Gylltoft (1994), Suresh (1998) or Dahlberg & Ekberg (2002).

Fatigue of materials was first observed and documented for iron. Suresh (1998) states that the first study of metal fatigue is believed to have been conducted around 1829 by the German engi-neer Albert (1838). He performed repeated load proof tests on mine-hoist chains made of iron. The interest in the study of fatigue expanded later on due to the increasing use of iron particu-larly in wheel axis and in bridges in railway systems, see e.g. general text books by Suresh (1998) and Frost et al. (1974). For concrete on the other hand, the fatigue phenomenon was observed rather late. According to Mallet (1991) the first fatigue curve for concrete cubes in compression was published by Van Ornum (1903). Van Ornum found no endurance limit for concrete similar to that which had been assumed for steel but he concluded that concrete had a fatigue strength about 55% of its static ultimate strength for a life of 7000 cycles. Hsu (1981) states that later on the development of highway systems in the 1920s led to further interest in the fatigue of con-crete, since the concrete pavements used for the highways are subjected to millions of load cycles from axle loads of cars and trucks.

The concrete fatigue research was later on intensified especially in Scandinavia during the 1970s. According to Gylltoft (1994) this was related to the oil industry and their many offshore structures that were exposed to forces from the sea.

During the last few years the concrete fatigue phenomenon has once again gained interest, es-pecially for railway bridges due to more slender structures, higher traffic speeds and higher axle loads. In Sweden for example, the increased axle loads on the existing railway lines have caused problems with the bridges since it has led to a change of the conditions for the bridges compared to the ones when they were built. One of the problems is that the bridges often are predicted to fail in the fatigue analysis when they are evaluated with the present concrete codes.

Over the years some Swedish fatigue tests have been performed. In Tepfers (1973) fatigue strength of overlap splices was studied, in Westerberg (1973) fatigue capacity of reinforced beams designed to fail in shear was tested (cited from Johansson (2004)), in Emborg et al. (1982) fatigue of cable couplings in prestressed beams was studied and in Ohlsson et al. (1990) fatigue strength

Fatigue

- 20 -

for unreinforced beams was tested for temperatures down to -35C. The latest tests seem to have been presented in Johansson (2004), where bridge deck fatigue tests were conducted in order to compare the results with predictions according to concrete codes.

4.1 Fatigue in General What is then a fatigue failure? Fatigue failure can be defined as a failure that occurs below the

stress limit of a material when it has been exposed to repeated loading. Some materials have a fatigue limit, which implies that below this load no fatigue failure will occur. Steel is such a material but for concrete no such limit has been detected (reports of a limit could be found though, see Hordijk (1991)). The reason for this difference is that steel is a strain-hardening material (the strength increases at large strains) and concrete is a strain-softening material (the strength decreases at large strains).

Fatigue tests are often very expensive and time-consuming to perform due to the many factors that influence the fatigue capacity. The many factors lead in turn often to great variation in the results. A few of the influencing factors are: material composition, load frequency, maximum load level, moisture content etc.

If a fatigue test only lasts a few load cycles it is named low-cycle fatigue (LCF). The limit that is used is approximate up to 103 (-104) load cycles. If the test lasts longer than this limit it is called high-cycle fatigue (HCF). There is also a third limit for a fatigue test, approximately 107 load cycles, called super-high cycle fatigue (SHCF) which is not so common. Many structures are subjected to fatigue loads. Some of them are bridges, roads, railway sleepers, offshore structures etc. The limits that have been mentioned here are not absolute ones, you can find other ones in the literature. In Figure 4.1 Hsu (1981) has given some examples of some structures and to which fatigue category they belong.

0 102 103101 105

NUMBER OF CYCLES

106 107 108104

5107 5108

MA

SS R

API

D T

RA

NSI

T

STR

UC

TU

RE

S

HIGHWAY AND RAILWAY BRIDGES,

HIGHWAY PAVEMENTS, CONCRETE

RAILROAD TIES

STRUCTURES SUBJECTED TO EARTHQUAKES

AIRPORT PAVEMENTS

AND BRIDGES

SEA

ST

RU

CT

UR

ES

SUPER-HIGH-CYCLE FATIGUE

HIGH-CYCLE FATIGUE LOW-CYCLE FATIGUE

Figure 4.1 Fatigue load spectrum according to Hsu (1981).

Hsu (1981) points out that it is important to look at the fatigue problem with a broad view and have in mind that rules and equations derived in research projects regarding high-cycle fa-tigue cannot be used in a study regarding low-cycle fatigue since the two ranges are different. Two reasons for this difference are the rate of loading and the effect of time in a fatigue test. Some researchers have claimed that the rate of loading is of no importance in a fatigue test but others have shown that it is of great importance regarding low-cycle fatigue. The same could be said regarding the effect of time in a fatigue test.

Fatigue

- 21 -

4.2 SteelThe fatigue behaviour of steel has been described in several textbooks, e.g. Suresh (1998),

Dahlberg & Ekberg (2002) or Gylltoft (1994). In Dahlberg & Ekberg (2002) the fatigue failure is described with three phases; crack initiation, crack growth and finally a brittle failure. The proc-ess starts with crack initiation and if the test continues these cracks will grow in size and a domi-nant crack will form with failure as consequence. If the failure surface is studied it is often possi-ble to identify two regions; a fairly smooth surface where the dominant crack has formed and the failure surface that is rougher.

Fatigue capacity is normally described by so-called Whler curves. They are named after the German engineer August Whler who conducted studies of the fatigue capacity of railway axles in the late nineteenth century, Whler (1858-1870). In Figure 4.2 results from fatigue tests are presented. If the loading of the material has a constant mean value and a constant amplitude then the fatigue life can be estimated directly from the Whler diagram of the material. The figure shows the number of load cycles for different applied amplitudes of stresses and as one can see the fatigue life decreases with increasing number of cycles. The curve is also sometimes called an S-N-curve (Stress-Number-curve). If the number of load cycles at failure, N, is presented on a logarithmic axle the curve becomes linear.

1 10 102 103 104 105 106 107

A

B

fat

One load cycle

Time

AAmplitude A

Figure 4.2 Number of load cycles N for different applied amplitudes of stresses, A. B is the static failure load. For e.g. steel, fat is the fatigue limit, if the loading does not exceed this limit no fatigue failure occurs, Elfgren & Gylltoft (1997).

The most well-known relationship when analysing steel fatigue is perhaps Paris law, Paris et al. (1961). In Shah et al. (1995) the equation is written as follows:

( )= FmFda C KdN (9) where the parameters CF and mF in Eq. (9) are experimental constants, da/dN is the crack

propagation rate and K is the stress intensity factor. It could also be written in logarithmic form:

= +F Flog log logda

m K CdN

(10)

4.3 Concrete Fatigue Unlike steel, concrete is not a homogeneous material. Already during the hardening process

micro cracks and air bubbles are formed. Mallet (1991) writes that fatigue of concrete is a pro-gressive process of micro-crack initiation and propagation leading to macro-cracks which can grow and determine the remaining fatigue life by causing stress to increase until failure occurs.

Fatigue

- 22 -

4.3.1 Influencing Factors

There are several factors that influence a fatigue test. Some of them are; the maximum stress level (often the live load), the lower stress level (often the dead load), the load amplitude, loading frequency (lower frequency gives lower number of cycles to failure) etc., see e.g Holmen (1979), Cornelissen (1986a), Mallet (1991), Srensen (1993) or Gylltoft (1994).

The load can also be varied in many ways in a fatigue test, see Figure 4.3. You can have pul-sating sinusoidal load (which implies that the mean stress, m, is equal to zero, see Figure 4.3a and the amplitude is a, the load can be the same as in example a) in Figure 4.3 but with a mean stress equal to the amplitude and min = 0. A more general case is shown in Figure 4.3c where m 0 and m min. There is also a type of loading called irregular loading which perhaps is the most correct type of loading a structure is exposed to, see Figure 4.3d. In this case it is a bit more difficult to decide loading cycle, mean value or the amplitude. There are several methods that can be used to determine these parameters for example the peak count method, range pair count or the rain flow count method. A description of the methods could be found in e.g. Mal-let (1991) or Dahlberg & Ekberg (2002).

stre

ss

time

a

a

a m

a) b) c) d)

min

max

Figure 4.3 Different types of loading that can be used in a fatigue test. Definitions: m =0.5(max+min), a = 0.5(max-min). Based on figures in Dahlberg & Ekberg (2002) and Gyll-toft & Elfgren (1977).

4.3.2 Refined Whler Curves

In order to improve the Whler curve Aas-Jakobsen (1970) examined the influence of the minimum stress, fmin, on the fatigue strength. He showed that the relationship between fmax/f and fmin /f is linear for fatigue failure at N = 210

6 load cycles. If R is defined as the ratio be-tween the maximum and minimum stress, fmax/fmin, then the relationship between fmax/f and Rshould also be linear (f equal to the static strength). Combining these linear relationships he derived the following expression:

( )max 1 0.064 1 log'

fR N

f= (11)

where = 0.064 ( is the slope of the S-N curve when R = 0). Eq. (11) is valid for 0 R 1, but not for stresses which alternate between compression and tension.

Tepfers & Kutti (1979) made an extensive study of Eq. (11) for ordinary concrete and light-weight concrete with the intention of proposing a fatigue relationship common for both types of concrete. They used experimental data from the literature (corresponding to log(N) = 6) and their own studies and proposed the following equation (see also the plot in Figure 4.4):

Fatigue

- 23 -

( )= maxc

'c

1 0.0685 1 logf

R Nf

(12)

where N is the number of loading cycles at fatigue failure, R is the ratio between the maxi-mum and minimum stress ( min maxc c/f f ),

maxcf is the highest compressive stress under pulsating

load, mincf is the lowest compressive stress under pulsating load and, finally, 'cf is the static

cylinder strength.

0 2 4 6 8 10log N

0

0.2

0.4

0.6

0.8

1f cm

ax /

f c'

( )= maxc

'c

1 0.0685 1 logf

R Nf

R = 1

R = 0.8

R = 0.6

R = 0.4

R = 0.2

R = 0

Figure 4.4 Graphical representation of Eq. (12). From Tepfers & Kutti (1979).

Tepfers & Kutti (1979) also pointed out that it is of great importance that if Eq. (11) is valid, Whler curves shall not be based on measurements where the amplitude or the lower stress

maxcf is kept constant, but on a constant

min maxc c/R f f= .

Hsu (1981) studied the work done by Aas-Jakobsen (1970) and Tepfers & Kutti (1979) and even though he considered Eq. (12) being a big step forward in the development of the S-N-curve, it had in his opinion two essential weaknesses. The first one is when R = 1, Eq. (12) becomes min maxc c/ 1f f = and fmax equals to a constant. He points out that this is theoretically incorrect because when R approaches unity a repeated load becomes a sustained load. It has by other researchers been established that sustained strength of concrete is time-dependent. There-fore time must be included in the relationship. The second weakness is that it does not include the rate of loading as a variable and this must be considered at least in low-cycle fatigue.

In order to eliminate these two weaknesses Hsu (1981) introduced the element of time into the relationship by introducing the third dimension of T, where T is the period of the repetitive loads expressed in seconds per cycle. By doing this, a three-dimensional space is created consist-ing of nondimensionalized f as the vertical axis with log N and log T as the two mutual perpen-dicular horizontal axes, see Figure 4.5a (f = ' 'st sus/f f , where

'susf is the sustained strength, or

discontinuity strength at 10 years, and 'stf is the static strength at a period of 1 sec/cycle). Hsu then drew a 45 diagonal straight line connecting these two axes and expressed the line by the equation (log N+log T) = constant, which leads to NT=constant where NT expressed the dura-tion of time of the repetitive loading. He could now draw a series of straight lines representing increasing duration of loading time.

Using the S-N-T space Hsu (1981) added the influence of time on the strength of concrete by using stress-time relationships found in the literature. Hsu (1981) plotted the curve FC1 in the f-N plane and the curve FB in the f-T plane with the help of stress-time relationships for sustained load strength found in the literature which corresponds to the case of cyclic loading when R=1, see Figure 4.5a. He then joined the points C1 and B and thereby created the surface FBC1. Fur-

Fatigue

- 24 -

thermore, again with the help of relationships found in the literature, the interaction surface ABC could be created for R=0 where the curve AB shows that the strength of concrete in-creases with increasing rate of stressing. In addition, the f-N curve AC was shown to have a steeper slope in the low-cycle region than in the high-cycle region which was consistent with observations that fatigue strength in low-cycle fatigue region is sensitive to the load duration and the rate of loading.

The two interaction surfaces ABC and FBC1 in Figure 4.5a then defined the cases of R=0 and R=1. A family of interaction surfaces could then be constructed between these two boundary cases by linear interpolation using R as the parameter.

Since these spaces that were created between the boundary conditions R=0 and R=1 were complex to describe, he simplified them into planes, see Figure 4.5b. The FBC1 surface in Figure 4.5a can be substituted with the FBC1 plane in Figure 4.5b, but the ABC surface for R=0 in Figure 4.5a should be approximated by the planes ABD (low-cycle region) and BDC (high-cycle region) in Figure 4.5b.

1 2 3 4 5 6 7 8 9

12

34

56

78

9

1.60

1.33

1.0

0

log T (sec/cycle)

log N (cycle)

C1

C

R=0

R=1R=0

R=1

R=1

R=0

B

A

fmaxfsus

G

F

fstfsus

ASTM LOADING RATE

1 2 3 4 5 6 7 8 9

12

34

56

78

9

1.60

1.333

1.0

0

log T (sec/cycle)

log N (cycle)

D

D1

C1

C

R=0

R=1

R=0

R=0

R=1

R=1

R=0

E

B

A

fmaxfsus

G

F

a) b)

Figure 4.5 a) Graphical representation of S-N-T-R relationship. b) Simplification of S-N-T-R relationship. From Hsu (1981).

Assuming that the transition from R=0 to R=1 was linear Hsu established two equations, one for high-cycle fatigue and one for low-cycle fatigue (Hsu also introduced an equation for the boundary between high-cycle fatigue and low-cycle fatigue). By introducing some assumptions and using data from the literature the following equations were established (see Hsu (1981)):

High-cycle fatigue:

( )max'c

1 0.0662 1 0.556 log 0.0294logf

R N Tf

= (13)

Low-cycle fatigue:

Fatigue

- 25 -

( )( )

max'c

1.20 0.20 0.133 1 0.779 log

0.053 1 0.445 log

fR R N

f

R T

=

(14)

where N is the number of loading cycles up to fatigue failure, R = fmin/fmax, fmax is the maxi-mum stress in repetitive loading, fmin is the minimum stress in repetitive loading,

'cf is the static

compression strength of concrete tested at ASTM loading rate and T is the period of the repeti-tive loads expressed in sec per cycle. Hsu (1981) mentions that it is generally accepted that if the maximum fatigue stress, max, is nondimensionalized by the static strength of an identical specimen, this nondimensionalized S-N curve (max/ versus log N) is independent of speci-men shape, the concrete strength, the curing conditions etc.

Hsu compared the equations with experimental data from the literature and the equations fit-ted the data rather well in some cases. Hsu has also examined the effect of T (the rate of loading) and found out that it had an influence but due to scatter of test results it could not be clearly established unless the difference in T was of two orders of magnitude. More thorough informa-tion can be found in Hsu (1981).

The model presented by Hsu (1981) was compared to three similar models by Srensen (1993), among them the model presented by Tepfers & Kutti (1979), see Eq. (12). Srensen (1993) was unable to decide which model that was most appropriate to predict the fatigue life for plain concrete. One observation that Srensen (1993) made, was that the proposal by Hsu (1981) predicts smaller slopes in the high-cycle region than in the low-cycle region, which is a phe-nomenon observed in the literature.

A model proposed by Stemland et al. (1990) was developed to predict the relation between Smax, Smin and N. The main intention with the constant amplitude tests performed on non-reinforced concrete by Stemland et al. (1990) was to evaluate the effect of the change in mini-mum stress level on the fatigue life. Their design proposal for fatigue in compression has the following formula:

( ) ( )2min min maxlog 12 16 8 1N S S S= + + (15) where, N is the number of load cycles, Smin is the minimum level of loading in one cycle (=

relative stress, reference stress is the static strength) and Smax is the maximum level of loading in one cycle(= relative stress, reference stress is the static strength).

As can be seen in Figure 4.6 the slope of the curves changes at log N = 6. They found that this is approximately where the experimental results started to deflect towards longer lives than indi-cated by the equation. They therefore proposed that log N greater than log N = 6 should be multiplied by the factor (based on Norwegian Code), X:

( )1 0.2 log 6X N= (16)

Fatigue

- 26 -

0.8

1.0

0.6

0.4

0.2

5 10 15 20 LogN

Smax

0.8

0.6

0.4

0.2

Smin=0

Log N=6

infinite lifetime beyond this curve

Figure 4.6 S-N diagram for fatigue of concrete in compression according to Stemland et al. (1990).

According to Srensen (1993) some positive features in this model are the distinction between the inclination in the low- and high-cycle region and the simplicity in practical use. One prob-lem with the model was that the time effects are omitted in case of low-cycle fatigue. For further information, see Stemland et al. (1990) or Srensen (1993). The model proposed in CEB-FIP (1993) is based on the model suggested by Stemland et al. (1990).

4.4 Accumulated Fatigue Damage, Palmgren-Miner A relation called the PalmgrenMiner rule can be used when estimating the accumulated fa-

tigue damage. The rule was first proposed by Palmgren (1924) and independently by Miner (1945), see also Mindess et al. (2002). It is convenient to use the rule as an approximation for high cycle fatigue and the rule suggests that failure occurs when:

i

i1

1I

i

n

N=

= (17)

Here ni is the number of load cycles at some stress condition and Ni is the number of load cy-cles required to cause failure at that condition. The rule assumes that there will be a linear accu-mulation of damage due to each loading cycle and that the hypothesis is not always conservative, i.e. it must be used with care.

Concrete Fatigue in Tension

- 27 -

5 Concrete Fatigue in Tension

In this chapter the tensile behaviour of concrete is described briefly and in papers C, D and E the described methods/models have been used. More information can be found in e.g. Cornelis-sen (1986a), Hordijk (1989), Hordijk (1991), Pinto (1996) or Noghabai (1998).

For concrete subjected to static compression load several studies have been performed over the years, but when it comes to tensile loading far fewer studies have been carried out. According to Hordijk (1989) the first publication demonstrating a post-peak behaviour of concrete under tensile loading is believed to be the one by Rsch & Hilsdorf (1963). One reason for the in-creased interest in the tensile behaviour of concrete was that fracture mechanics began to be used for concrete structures in order to understand and describe the mechanisms of cracking.

Even though nowadays the tensile strength of concrete is neglected in many design codes, it is of importance. Because, as pointed out by Cornelissen (1986a), the tensile strength governs the cracking behaviour and therefore also, e.g. the stiffness, the damping action, the bond to embed-ded steel and the durability of concrete. The tensile properties are also of importance when it comes to shear capacity of concrete.

5.1 Tensile Behaviour of Concrete and Fracture Mechanics In order to describe the phenomenon of cracking of concrete in tension researchers started to

use fracture mechanics, methods that had been used since the 1940s for metals and glass. Fracture mechanics methods study the conditions in the area in front of and around a crack tip. There are several text books on the subject of fracture mechanics of concrete, e.g. Elfgren (1989) or Baant & Planas (1998).

In Pinto (1996) the tensile behaviour of concrete is very well explained with the help of Figure 5.1: In Figure 5.1 a deformation controlled centric tension test is performed on a speci-men, where the specimen is loaded with the force P and the total deformation is measured over the length l. At the left side of Figure 5.1 the specimen is plotted for the load steps A, B and C. The load steps are also marked in the load-deformation curve at the right side. Load step A is before peak load, load step B at peak load and load step C after the peak load in the descending branch of the load-deformation curve. Already before the peak load is reached, some micro-cracking occurs see Figure 5.1a. As the microcracking is uniformly distributed at the macrolevel, a uniform strain over the length of the specimen may be assumed. The strain is plotted over the length of the specimen in Figure 5.1 right next to the specimen. Immediately before the


- 28 -

peak load, an accumulation of micro cracks occurs at the weakest part of the specimen. At the macrolevel this leads to an additional strain over the length h of this weak part. A crack band (also called process zone or softening zone) of width h develops, see Figure 5.1b. Having passed the peak load, the crack band localizes more and more. The crack band width diminishes, and the deformation within the crack band increases. The final failure occurs due to one single crack.

Pinto (1996) states that the total deformation of the specimen may be split up in the bulk de-formation - which is almost linearly elastic up to the peak load and the deformation of the crack band. Just before the peak load is reached, between point A and B in Figure 5.1, the relationship bends off from the linear behaviour. Where the non-linear behaviour starts to devi-ate varies between the studies performed in the literature. According to Pinto (1996) these dif-ferences in the experimental results are caused by different boundary conditions. Any source of non-uniformity, like internal bending due to non-uniform cracking, eigenstresses due to differ-ential shrinkage and temperature, notch effects etc. causes nonlinearities.

x

h*

h

x

x

A

B

C

P

P

(a) (b)

l

P/A

=

w = ll

(c)

l

C

AB

P/A

=

l

l

l

Figure 5.1 The tensile behaviour of concrete. Based on figure in Pinto (1996).

In Pinto (1996) some suggestions are presented for the -w relation in the case of monotonic loading, see Figure 5.2.

wcw

ct/f c

t

1

a)

wcw

1

b) w

1

c)

wcw

1

e)

Figure 5.2 Suggestions for the -w relation: (a) linear, (b) bilinear Petersson (1981), (c) mul-tilinear Gustafsson (1985) and (d) Cornelissen et al. (1986). Based on Pinto (1996).


- 29 -

5.2 Fictitious Crack Model The classical concept of fracture mechanics was not appropriate for concrete because, as for-

mulated by Mihashi & Rokugo (1998), concrete is a kind of composite and a very heterogene-ous material (compared to glass and metals). Therefore, cracks are arrested when they encounter aggregates and a large fracture process zone is developed in front of the main crack

Date post:	12-Oct-2015
Category:	Documents
Upload:	marcob74
View:	25 times
Download:	1 times

Thun 2006 - PhD Assessment of Fatigue Resistance And

Documents